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Abstract：
In order to comprehend the dynamics of disease propagation within a society, mathematical formulations are essential. The purpose of this work is to investigate the diagnosis and treatment of lung cancer in persons with weakened immune systems by introducing cytokines ( I L 2 & I L 12 ) and anti-PD-L1 inhibitors. To find the stable position of a recently built system TCD I L 2 I L 12 Z, a qualitative and quantitative analysis are taken under sensitive parameters. Reliable bounded findings are ensured by examining the generated system\'s boundedness, positivity, uniqueness, and local stability analysis, which are the crucial characteristics of epidemic models. The positive solutions with linear growth are shown to be verified by the global derivative, and the rate of impact across every sub-compartment is determined using Lipschitz criteria. Using Lyapunov functions with first derivative, the system\'s global stability is examined in order to evaluate the combined effects of cytokines and anti-PD-L1 inhibitors on people with weakened immune systems. Reliability is achieved by employing the Mittag-Leffler kernel in conjunction with a fractal-fractional operator because FFO provide continuous monitoring of lung cancer in multidimensional way. The symptomatic and asymptomatic effects of lung cancer sickness are investigated using simulations in order to validate the relationship between anti-PD-L1 inhibitors, cytokines, and the immune system. Also, identify the actual state of lung cancer control with early diagnosis and therapy by introducing cytokines and anti-PD-L1 inhibitors, which aid in the patients\' production of anti-cancer cells. Investigating the transmission of illness and creating control methods based on our validated results will both benefit from this kind of research.
摘要：
为了理解社会中疾病传播的动态，数学公式是必不可少的。这项工作的目的是通过引入细胞因子（IL2＆IL12）和抗PD-L1抑制剂来研究免疫系统减弱者肺癌的诊断和治疗。为了找到最近建立的系统TCDIL2IL12Z的稳定位置，在敏感参数下进行定性和定量分析。通过检查生成的系统的有界性来确保可靠的有界发现，积极性,独特性,和局部稳定性分析，这是流行病模型的关键特征。具有线性增长的正解被全局导数验证，使用Lipschitz标准确定每个子隔室的影响速率。使用具有一阶导数的Lyapunov函数，为了评估细胞因子和抗PD-L1抑制剂对免疫系统较弱的人的联合作用，检查了该系统的整体稳定性。通过使用Mittag-Leffler内核与分形分数算子相结合来实现可靠性，因为FFO以多维方式提供了对肺癌的连续监测。为了验证抗PD-L1抑制剂之间的关系，使用模拟研究肺癌疾病的症状和无症状效应。细胞因子,和免疫系统。此外，通过引入细胞因子和抗PD-L1抑制剂，通过早期诊断和治疗来确定肺癌控制的实际状态，这有助于患者产生抗癌细胞。根据我们验证的结果调查疾病的传播并创建控制方法都将从这种研究中受益。
